Here is the grid at the end of a bypass exceptional among Nakamoto Extreme puzzles.

The slink marking bypass is a human engineering feature that replaces the burdensome candidate identification task most experts cede to the computer, with an enjoyable challenge.

Beyond the naked pairs that claim cells in the bypass, strong link and subset marking are completed in two more systematic stages: box marking and line marking.

Short of AIC building, Sudokuwiki finds only this simple XY ANL, shown here on the line marked grid.

In AIC building, the new c2 7-slink allows an ALS bv boomerang.

That proves enough to get constructive methods going again.

The new r2 7-slink allows another XY.

The new bv prompts a Sudokuwiki simple coloring trap. In the trap, 5r4c8 is removed by green and by blue. Leave the cluster to possibly expand.

Update the 5-panel, but also look to see what the removal does. Here it creates a grouped slink for a 5-chain ANL.

After W2 and E2,

Sudokuwiki opens a second simple cluster for a trap.

The trap expands red/orange to show:

not (blue and range) => green or red

It also enables an XY ANL removing 8 and bringing 7 into red/orange.

After

a 347-wing and a very striking BARN.

The expansion wraps red in r5c3, and recall that red or green must be true, so orange and green are confirmed.

Next, its Nakamoto Extreme 143.

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The starting cluster is expanded when West to East freeforms reveal that any pattern including 4r1c1 also includes 4r3c7. In other words, if blue 4r5c1 is false, then 4r3c7 is true, defining a slink carrying the colors across the grid to trap 4r1c3.

After this expansion, West to East freeforms for blue confine it to a single pattern, and the cluster wraps green, as two green 4’s are forced into c3, with follow up:

Now AIC building is unnecessary. First comes an XY-chain removing 6r6c4.

Then another for 7r4c5:

After a third ANL triggers a SEr9 boxline,

a large second cluster can be added, just in time for a shortcut confirming ANL.

This sets up the identical confirming ANL from the Sudokuwiki path, but this time, for the collapse, as orange 9r5c5 wraps red.

The collapse trace and color version of the solution are below.

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Nakex 103 starts a little differently, with some bypass success:

Also untypical in Nakamoto Extreme is an X-wing in the third stage of basic line marking.

The 5-wing appears when the two 5’s in r6 are seen to match columns with the naked pair of r8. The fish icons are left to affect the line marking of c2, c5, and the closure rows.

The basic trace of Nakex 103:

The first Sudokuwiki move on this grid is an APE in which an 5-value ALS eliminates combination 31 and a bv, the 41.

How is such a large APE partner ALS suggested? Other than the bv, 1r3c9 has only one combination with r3c7, 31 in r3c8. Now from r3c8, you stretch the ALS boundaries along r3 to get one ALS containing 31.

With that, Sudokuwiki now enters AIC building, missing the pink/olive pattern analysis on the 4-panel to be shown in the next post. Will your version of that ready for comparison?

For this AIC confirming ANL, you might start with the r4 4-slink from 4r4c6, noticing the AIC wink to the W grouped 3-slink. The wink to 3r5c9 and AIC wink gets you to the 4-chain leading around to the C grouped slink closing the ANL. C4=> S4, and the “bunny rabbit” just happened.

The next just happening is an AIC nice loop. 5r5c3 is a good start for a boomer, and Medusa XY cells carry the ball, but the 4-slink back into the starting cell closes the nice loop. The same description applies to a boomer start from 4r5c3.

Then an alternate path from 4r5c1 achieves boomerang 1.

Independently, a second boomer, from 5r6c5, re-traces a section of boomer 1.

Any emerging slink, however long, is eligible to start a boomerang. Here, the grouping creates the r6 slink necessary to get back to the starting cell of boomer 3.

Sudokuwiki labels boomer 4, in black, as a digit forcing chain, removing 2r9c4 regardless of 4r3c7 being true or false. But arriving at that conclusion by choosing a candidate in the boomer is blind luck. The boomer starts with the 6-slink from r9c4, and the cluster supports the shortcut in red.

The boomer 4 removal enables this confirming AIC ANL, starting from either slink from 9r1c3. The NW9 placement removes 2r1c3, allowing an extensive cluster to develop. This cluster is an immediate result of the 4-panel pattern analysis to be covered next post.

In fact, the next Sudokuwiki move is an AIC confirming ANL that is also the final move in the shortened solution path next week.

But not here. After the follow up

Sudokwiki continues with a hidden unique rectangle, Type 2b. and an XY ANL.

Next, three moves on a grid. First , the West BARN 3467 removes 6r6c1. This removes 7r5c1, by the naked triplw 178, or by turning 6r5c1 green for a trap. The 7 chain stands alone with one elimination 7r9c3, which enables the purple BARN 1238.

Ending this Sudukowiki display in a Sysudoku way, a bv boomer from 6r1c1 wraps green.

Even so, it still leaves a 273-wing to put Nakamoto 103 away.

But not until next week, when you compare your shorter version to the one appearing here.

]]>From the first cluster trap and BARN, further expansion and the aligned triple continue to move Nakamoto Extreme 83 towards the exit door.

In particular, the second aligned triple’s 4r8c1 removal brings a second BARN, and its expansion traps below

The follow up

brings a third BARN, and that BARN’s removals set up

a fourth.

Then after a shortcut XY ANL (left) expands the cluster for three more traps

the next expansion wraps green in c6, for the immediate collapse of Nakamoto Extreme 83.

Next time, it’s Nakamoto Extreme 103.

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The line marked grid is evidence of the extremely tough basic phase, with many long line fill lists and cells of four and five candidates.

The basic trace reports no concessions.

Heavy lifting continues as Nakex 83 requires immediate AIC building. Here is AIC boomer 1 turned confirming ANL, from 2r1c3. It ties 2 and 3-chains together with AIC winks.

A second confirming ANL follows the same spotting pattern, two converging slinks, starting as a boomerang from 3r3c1.

After the follow up

,

the naked pair C47 removes two 7’s from the C box, the aligned triple W7t removes 7r8c2, and an XY ANL removes two 4’s.

Now, starting from the new 7-slink in the r5s57 pair, an ALS node and XY segment lead back to the starting 7 for a nice loop.

Nakex 83 is showing that boomer search is a basis for all AIC building, and there is good reason to keep up with bv scanning data.

After

a budding cluster nets a trap, and an XY ANL, to which Sudokuwiki adds a BARN.

For newcomers, a BARN is a Bent Almost Restricted *n*-set.

An *n*-set is *n* cells containing only *n* values. In this and most cases, *n* = 4. “Restricted” here means confined to one unit, box or line. “Almost” refers to one of the values being bent to share two units, a bent region. In a BARN the bent value is toxic. It includes a true value.

From here, Nakamoto Extreme 83 finishes with coloring expansions and traps, generating a series of three more BARNs and two shortcut ANL. Using Sudokuwiki, I missed out on finding them, but you don’t have to. It’s laid out next week.

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Sudokuwiki doesn’t maintain coloring clusters between moves, or use pattern analysis to expand them. After the 785-wing in the solution of the previous post, Sudokuwiki continued with a two solution paths too instructive to pass up.

The first continues with an Andrew Stuart *cell forcing chain*. The idea is to remove a candidate that forces all candidates in some cell to be false. It takes a modern computer very little time to determine what a single candidate forces out, but how many such examinations fail between cell forcing chain successes? Way too many for human tolerance.

But here’s one. 3r1c9 forces 7r8c2 off via 3-chain and 7-chain. The ALS forces 1r8c1 on, 15r8c1 off. Is that a peacock or a swan?

The 3r1c9 removal enables a confirming ANL enlisting a UR slink and an ALS node. What is a UR slink? The rectangle r89c16 presents a multiple solution if both 3r8c1 and 6r9c1 are false. Therefore, If one is false, the other must be true. A strong link in the ANL.

Now, after a simple BARN,

two hidden unique rectangles, Type 2.

Next, an APE, in which the ALS excludes 15, and the bv at r4c1, 35, as placement combinations in the aligned cells.

Then an ALS AIC nice loop expands the cluster to trap 9r6c3 and bring in C8.

The further expansion traps four candidates and repeats the XY-wing of the last post.

The follow up to E5 proves green to finish Nakamoto 63 the Sudokuwiki way.

Andrew Stuart’s Sudokuwiki solver has an option to bypass specific methods. When Stuart’s *cell forcing chain* is bypassed, the next method after boomer 7 and the 785-wing is this ALS toxic pair. 3r9c1 is eliminated because it sees all 3’s in both ALS. Since only one ALS can have a 7, all values are locked in one of the ALS, including one of those 3’s. The toxic pair takes the place of the cell forcing chain in the Sudokuwiki solution path.

But a second elimination, of 9r6c3, Sudokuwiki attributes to “rule 2”, saying 2,4,9 are unique to the orange ALS. We need to know what prevents 9r6c3, and therefore blue, from being true, and leaving the ALS placements 2, 3,4, and 7?

In Stuart’s Sudokuwiki strategies, “rule 2” is attributed to forum guru David Bird, but not explained. A clue to rule 2 is the fact that 9r6c3 forces both shared 3’s in the SW box to be true. That is because it forces 9 out, and 7 into the orange ALS, along with 3 and 2.

In general terms, this effect can be described this way:

The reason is, when an unshared value is removed, it forces the common value into its ALS, removing the common value from the other ALS, and leaving both ALS locked. In the above example, 9r6c3 must go because single 3’s in both ALS share a box and can’t both be true.

It’s not that that the outside candidate can’t be true, removing a value set. It’s that the effect that has in this case violates Sudoku placement restrictions.

Next week, we consider what Sudokuwiki can do with Nakamoto Extreme 83. You must have the book by now. Are you using another human oriented solver? If so, tell us about it.

]]>Nakex 63 basic is tough, despite a productive bypass.

The first advanced move is one 3-chain ANL, extended by a NWc2 boxline, and into a longer one.

Getting to the 9-panel, grouping makes a slink in r4. The victim sees the grouped terminal in the East box.

After planting a cluster, we follow Sudokuwiki into AIC building with an easy AIC boomerang 1 from 3r4c1.

The removal expands the cluster in c1. In fact, looking at the 9-panel,

the new c1 slink brings the slinks from 9r3c1 to three, and winks from two of them bring to five the number of 9’s that are true if 9r3c1 is false.

Translated to coloring, two green patterns and one blue one are expanded, as four traps become orphans. A pink/olive result in blue and green

Sudokuwiki doesn’t see the pattern eliminations or the naked triple and hidden UR they bring, but goes ahead with the boomer parade. Next, from 8r6c5 an XY node and a reversed bv three X-chains tied together for AIC boomer 2.

Boomer 3 in the parade, from 3r9c3. In building a boomer, after every slink you try possible winks, going with any that reach another slink, or a starting cell candidate. You can see the destination slink in every transition here.

We don’t report on the stalls, like 3r6c1 after the starting slink. There are no more stalls here after we reach 5r4c1. This is the second of four possible continuations, working clockwise. If all AIC after 5r4c1 fail, there are two possible wink/slink continuations remaining, to 3r6c4, and to 3r6c5.

Along the way, there are two possible return targets here, 2 and 7.

It takes persistence to explore all possible return paths. Many of them fail, and some after considerable effort. But there is a systematic process that is humanly accessible.

Boomer 4 looks like an ANL requiring a different spotting process. But no, it’s also a boomerang, from 3r8c8, coming back on a grouped 5-chain.

Next in the parade is the backup float. Starting with a long boomer 5 from 2r9c2, back up one slink to traverse the AIC in the opposite direction, hopping off to look back in the opposite direction for boomer 6.

Instead of the mayor in a convertible, now we get a grouped AIC ANL.

The boomer spell is decisively broken when the ANL removals enable the finned swordfish below.

The logic is: if the extra candidate spoiling the fish is seen by the victim, then were the victim to be true, its vision would remove the fin, making the fish valid and victim toast. If the victim and fin share a box or line, call it a finned fish. If the wink is an inference chain, call it a kraken fish.

Sudokuwiki can now return to the parade. It gets boomer 7 from 8r7c9, which gains a bv,

that enables a 785-wing in East.

The expansion traps 8r4c5 and 8r6c9 bring C8 and an XY wing, enabling

a simple 5-chain ANL (red), followed by XY ANL that destroys one of its nodes. N5 is confirmed as a hidden single in E or r6., whereupon

E5 => SE8 wraps blue, and the green army mops up Nakamoto Extreme 63.

Next week, we follow two Sudokuwiki paths from the 785-wing, without the pattern analysis or recorded coloring. One path is humanly practical and one isn’t.

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As often happens a short basic trace

signals a cloudy starting grid.

Before bringing out the boomerangs, Nakex 43 throws us an easy X-chain.

And here they come. Boomer 1 from 5r4c6 and boomer 2 from 9 r9c6. Even though both are X-chains linked by XY bv nodes, they are found in AIC building, where any means of extending a chain are employed.

Next come AIC boomers 3 from 8r1c4 and 4 from 6r1c6 => NWr1 boxline 2r3c2 and AIC boomer 5 from 1r2c8 creates NWr2 boxline removing 9’s.

Then AIC boomer 6 from 3r1c3.

The removal allows the former boomer path into 3r1c3 for an ANL removing 3r1c4. Then extension (red) from 8r1c4 closes ANL confirming 3r1c3.

The confirmed NW3 goes nowhere, but boomer 7 from 6r1c6 finds an ALS to get home, for N6.

After two XY ANL => NW9, an XY boomer 8 from 8r6c5.

Next, AIC boomers 9 from 9r8c5 and 10 from 2r5c8. The boomer 10 removal permits

a 6-chain ANL, and the new 6-slink in r5, which brings boomer 11.

The 6-chain removal also enables AIC boomer 12 from 6r4c9, and the boxline SEr9. To the left, the grouped boomer 13.

Sudokuwiki mislabels AIC bv boomer 14, from 2r1c1, as a digit forcing chain. The interpretation does not lead to a humanly practical way to find it. Viewing it as a boomerang does precisely that.

After

,

Sudowiki finds an APE requiring three ALS, a very unlikely human solving event. But the removal is not needed until much later.

Instead, the next AIC ANL depends on boomer 10.

The AIC ANL creates the c6 3-slink for a confirming bv boomerang 15.

After

,

the removal brings a long XY chain. But coloring is past due.

The cluster makes a shortcut example of the next XY chain, as the former XY removal enables a grouped 9 chain.

The 9-chain removal expands the cluster, trapping 8 to continue the expansion and force two blue candidates in r8c4. The green army cuts through the candidate undergrowth and lays out the Nakamoto Extreme 43 solution for us.

Thanks for sticking with a a very long post. I found no logical escape hatch, but perhaps you did. If so, clue us in. I’ll publish your comment, diagram your find, from your what and where, in a following post.

Next , another two post effort is Nakamoto Extreme 63. There’s another boomerang parade, then the first post ends it with Sysudoku pattern analysis and coloring, leaving the less spot worthy, but more spectacular, Sudokuwiki ending for the second post. You could follow the parade with Sudokuwiki, looking critically at your X-panels to see if you can get that first ending before it comes out here.

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Leaving the original Sudokuwiki grouped AIC boomerang 9 without invoking the blue wrap extensions, Andrew Stuart’s solver finds boomers 10 and 11 incorporating the same grouped slink.

Then comes two rare sights together, a regular XYZ-wing and boomer 12 with an ALS node.

Still counting, a grouped boomer 13 from 2r2c9.

Building on that, Sudokuwiki calls this a *digit forcing chain,* making 1r5c5 true whether 9r1c3 is true or false.

Picking 9r1c3 is misleading. The same attribution can be made for any other candidate along the loop.

The conclusion actually comes from the loop itself. It is a confirming almost nice loop, an ANL, asserting green.

Next week, Sysudoku Basic and Sudokuwiki advanced for Nakamoto Extreme 43.

]]>The Nakex 23 line marked grid and basic trace:

After a quick scan for unique rectangles or remote pairs, a sysudokie constructs a bv map for XY chains and makes a copy for XYZ wings.

That is rewarded here with a inference chain i571-wing. Finding that a 17 bv is present to accompany the 15 wing, its not hard to find a 7-chain for the weak link. Sudokuwiki doesn’t do inference chain winks.

A coloring cluster looks promising. Green or blue removes 7r2c5.

The i571-wing removal is duplicated by an XY ANL following up the trap. Sudokuwiki misses both, but finds an APE removing 1r9c3. ALS 157 prohibits 71 and ALS 129 bans 91. The two removals in c3 expands the cluster.

The cluster expansion traps 1r5c2 and provides a shortcut boomerang from 6r9c3, beginning a boomerang volley with boomer 2 below from 3r3c8 in black.

Boomer 3 in red branches off to come back at 6r3c8, and boomerang 4 (green) is thrown in the opposite direction from the 8-chain to another 3-chain.

The new bv 31r3c8 completes an XY ANL for NE3.

Then another boomer barrage, with boomer 5 from 2 r2c9 in black, boomer 6 from 9r1c9 in red, boomer 7 from 1r1c2 in green, and boomer 8.

The 9r1c2 removal allows a grouped AIC ANL.

Next is Sudokuwiki’s grouped boomer with a group as the emerging slink partner.

The Sysudoku cluster reveals a remarkable coloring wrap. The red extensions create an inference chain weak link between cluster members of the same color. If one is true, the other is false. Being the same color, both must be false, and blue is wrapped. Wow!!

From here, it still takes a naked triple, and two 1-ANL to wrap up Nakamoto Extreme 23.

Next post will forego the wrap and continue Sudokuwiki’s path to the end, for two purposes. First, to graphically reveal more beautiful boomerangs, and second, to reveal the Sudokuwiki “digit forcing chain”. If you’re solving ahead of the blog for the feedback, here is an opportunity to find these gems on your own.

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